Rapid advances in high-throughput sequencing facilitate variant discovery and genotyping, but linking variants into a single haplotype remains challenging. Here we demonstrate HaploSeq, an approach for assembling chromosome-scale haplotypes by exploiting the existence of \&$\#$39;chromosome territories\&$\#$39;. We use proximity ligation and sequencing to show that alleles on homologous chromosomes occupy distinct territories, and therefore this experimental protocol preferentially recovers physically linked DNA variants on a homolog. Computational analysis of such data sets allows for accurate (\∼99.5\%) reconstruction of chromosome-spanning haplotypes for \∼95\% of alleles in hybrid mouse cells with 30\× sequencing coverage. To resolve haplotypes for a human genome, which has a low density of variants, we coupled HaploSeq with local conditional phasing to obtain haplotypes for \∼81\% of alleles with \∼98\% accuracy from just 17\× sequencing. Whereas methods based on proximity ligation were originally designed to investigate spatial organization of genomes, our results lend support for their use as a general tool for haplotyping.